Attenuation of shear sound waves in jammed solids

TL;DR

This paper investigates how shear sound waves are attenuated in jammed solids, revealing a power-law scaling of attenuation with frequency and packing fraction near the rigidity transition, supported by numerical evidence.

Contribution

It introduces a model linking attenuation scaling to the divergence of domain sizes in jammed packings near the critical point.

Findings

Attenuation coefficient follows Rayleigh law with lpha()  ^4 ( - _c)^{-5/2}

Characteristic frequency ^* scales as ( - _c)^{1/2}

Domain size diverges as ( - _c)^{-1/2} near transition

Abstract

We study the attenuation of long-wavelength shear sound waves propagating through model jammed packings of frictionless soft spheres interacting with repulsive springs. The elastic attenuation coefficient, $\alpha(\omega)$, of transverse phonons of low frequency, $\omega$, exhibits power law scaling as the packing fraction $\phi$ is lowered towards $\phi_c$, the critical packing fraction below which rigidity is lost. The elastic attenuation coefficient is inversely proportional to the scattering mean free path and follows Rayleigh law with $\alpha(\omega)\sim \omega^4 (\phi - \phi_c)^{-5/2}$ for $\omega$ much less than $\omega^* \sim (\phi - \phi_c)^{1/2}$, the characteristic frequency scale above which the energy diffusivity and density of states plateau. This scaling of the attenuation coefficient, consistent with numerics, is obtained by assuming that a jammed packing can be viewed as a mosaic composed of domains whose characteristic size $\ell^ * \sim (\phi-\phi_c) ^{-1/2}$ diverges at the transition.